Simplify the following expression: $ z = \dfrac{t + 6}{-9t} - \dfrac{-6}{5} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{t + 6}{-9t} \times \dfrac{5}{5} = \dfrac{5t + 30}{-45t} $ Multiply the second expression by $\dfrac{-9t}{-9t}$ $ \dfrac{-6}{5} \times \dfrac{-9t}{-9t} = \dfrac{54t}{-45t} $ Therefore $ z = \dfrac{5t + 30}{-45t} - \dfrac{54t}{-45t} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{5t + 30 - 54t }{-45t} $ Distribute the negative sign: $z = \dfrac{5t + 30 - 54t}{-45t}$ $z = \dfrac{-49t + 30}{-45t}$ Simplify the expression by dividing the numerator and denominator by -1: $z = \dfrac{49t - 30}{45t}$